Determine the length of the latus rectum of the parabola y^2 = 16x.
Practice Questions
Q1
Determine the length of the latus rectum of the parabola y^2 = 16x.
4
8
16
32
Questions & Step-by-Step Solutions
Determine the length of the latus rectum of the parabola y^2 = 16x.
Step 1: Identify the standard form of the parabola. The given equation is y^2 = 16x.
Step 2: Compare the given equation with the standard form y^2 = 4px. Here, 4p = 16.
Step 3: Solve for p by dividing both sides of the equation 4p = 16 by 4. This gives p = 4.
Step 4: Use the formula for the length of the latus rectum, which is 4p.
Step 5: Substitute p = 4 into the formula: Length = 4 * 4 = 16.
Parabola Properties – Understanding the standard form of a parabola and the relationship between its parameters, specifically how to derive the length of the latus rectum.
Latus Rectum Calculation – Applying the formula for the length of the latus rectum, which is 4p for parabolas in the form y^2 = 4px.
